Brain age is the estimate of biological age derived from neuroimaging datasets using machine learning algorithms. Increasing brain age with respect to chronological age can reflect increased vulnerability to neurodegeneration and cognitive decline. In this paper, we study NeuroVNN, based on coVariance neural networks, as a paradigm for foundation model for the brain age prediction application. NeuroVNN is pre-trained as a regression model on healthy population to predict chronological age using cortical thickness features and fine-tuned to estimate brain age in different neurological contexts. Importantly, NeuroVNN adds anatomical interpretability to brain age and has a `scale-free' characteristic that allows its transference to datasets curated according to any arbitrary brain atlas. Our results demonstrate that NeuroVNN can extract biologically plausible brain age estimates in different populations, as well as transfer successfully to datasets of dimensionalities distinct from that for the dataset used to train NeuroVNN.